Analysis of a post-fracture - Constant-rate flow test with boundary effects

Input(s)

\(\mathrm{q}_{\mathrm{g}}\): Gas Flow Rate (MSCF/day)

\(\mathrm{B}_{\mathrm{g}}\): Gas formation Volume Factor \((\mathrm{RB} / \mathrm{MSCF})\)

\(\mathrm{m}\): Slope from Curve (psi/cycle)

\(\mathrm{m}_{\mathrm{L}}\): Slope from linear Region of Curve (psi/cycle)

\(\mathrm{p}_{\mathrm{ai}}\): Initial Adjusted Well Pressure (psi)

\(\mathrm{p}_{\mathrm{ahr}}\): Adjusted Well pressure at \(t=1 \mathrm{~h}(\mathrm{psi})\)

\(\mathrm{p}_{\mathrm{D}}\): Dimensionless Pressure (dimensionless)

Ø: Porosity (dimensionless)

\(\mathrm{c}_{\mathrm{t}}\): Compressibility (1/psi)

\(\mathrm{r}_{\mathrm{w}}\): Radius of Wellbore \((\mathrm{ft})\)

\(\mu\): Viscosity \((\mathrm{cP})\)

\(\mathrm{h}\): Formation Thickness ( \(\mathrm{ft}\) )

\(t_{L f D}\): Time of end of Linear or Pseudo Radial flow from Plot (dimensionless)

\(\Delta \mathrm{t}_{\mathrm{a}}\): Adjusted Delta Time from Derivative Curve (h)

Output(s)

\(\mathrm{k}\): Permeability \((\mathrm{mD})\)

\(\mathrm{L}_{\mathrm{fPR}}\): Length of Fracture for Pseudo Radial Flow (ft)

\(\mathrm{L}_{\mathrm{fL}}\): Length of Fracture for Linear Flow (ft)

\(\mathrm{L}_{\mathrm{fMP}}\): Length of Fracture from Match Point Analysis \((\mathrm{ft})\)

\(\mathrm{s}\): Skin Factor (dimensionless)

\(\Delta \mathrm{P}_{\mathrm{a}_{\mathrm{MP}}}\): Adjusted Pressure Difference at Match Point from Plot (psi)

Formula(s)

Reference(s)

Lee, J., Rollins J.B., and Spivey J.P. 2003, Pressure Transient Testing, Vol. 9, SPE Textbook Series, Vol. 9, Henry L. Doherty Memorial Fund of AIME, Richardson, Texas, SPE, Chapter: 6, Page: 121.